共查询到20条相似文献，搜索用时 640 毫秒
1.
Alessandra Celletti Fabrizio Paita Giuseppe Pucacco 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):15
We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree-of-freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families. The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase plane of the normal form, we can identify a Laplace-like configuration, which highlights many substantial aspects of the observed one. 相似文献
2.
The scalar equations of infinitesimal elastic gravitational motion for a rotating, slightly elliptical Earth are always used
to study the Earth's nutation and tides theoretically, while the determination of the integration of the equations depends,
to a certain extent, on the choice of a set of appropriate boundary conditions. In this paper, a continuity quantity related
to the displacement is first transformed from the elliptical reference boundary to the corresponding effective spherical domain,
and then converted from a vector (or tensor) form to a scalar form by generalized surface spherical harmonics expansion. All
the related components, including the displacement vector field (or the stress tensor field), are then decomposed into the
poloidal and toroidal field using the symmetry restrictions on the normal mode eigenfunctions. After truncation, the boundary
conditions are finally derived, in a scalar ordinary differential form. The process of the derivation is second order in ellipticity
and in full detail. Moreover, the other boundary conditions are also presented as second order in ellipticity at the end of
this paper.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
Scale-free discs have no preferred length or time-scale. The question has been raised whether such discs have a continuum of unstable linear modes or perhaps no unstable modes at all. We resolve this paradox by analysing the particular case of a gaseous, isentropic disc with a completely flat rotation curve (the Mestel disc) exactly . The heart of the matter is this: what are the correct boundary conditions to impose at the origin or central cusp? We argue that the linear stability problem is ill-posed and that similar ambiguities may afflict general disc models with power-law central cusps. From any finite radius, waves reach the origin after finite time but with logarithmically divergent phase. Instabilities exist, but their pattern speeds depend upon an undetermined phase with which waves are reflected from the origin. For any definite choice of this phase, there is an infinite but discrete set of growing modes. The ratio of growth rate to pattern speed is independent of the central phase. This ratio is derived in closed form for non-self-gravitating normal modes and is shown to agree with approximate results obtained from the shearing sheet in the short-wavelength limit. This provides the first exact, analytically solved stability analysis for a differentially rotating disc. For self-gravitating normal modes, the ratio of growth rate to pattern is found numerically by solving recurrence relations in Mellin-transform space. 相似文献
4.
Giuseppe Pucacco Dino Boccaletti Cinzia Belmonte 《Celestial Mechanics and Dynamical Astronomy》2008,102(1-3):163-176
The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attention is focused on the quantitative predictive ability of the normal form. We find analytical expressions for bifurcations of periodic orbits and compare them with other analytical approaches and with numerical results. The predictions are quite reliable even outside the convergence radius of the perturbation and we analyze this result using resummation techniques of asymptotic series. 相似文献
5.
J. S. Watson G. D. Mistretta N. L. Bonavito 《Celestial Mechanics and Dynamical Astronomy》1975,11(2):145-177
In order to retain separability in the Vinti theory of Earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all, altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program.Results of this technique for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by this theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time. 相似文献
6.
Liam M. Healy 《Celestial Mechanics and Dynamical Astronomy》2003,85(2):175-207
The Lie transfer map method may be applied to orbit propagation problems in celestial mechanics. This method, described in another paper, is a perturbation method applicable to Hamiltonian systems. In this paper, it is used to calculate orbits for zonal perturbations to the Kepler (two-body) problem, in both expansion in the eccentricity and closed form. In contrast with a normal form method like that of Deprit, the Lie transformations here are used to effect a propagation of phase space in time, and not to transform one Hamiltonian into another. 相似文献
7.
We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce
suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian
coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a
kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form
up to 40th order in Cartesian coordinates. 相似文献
8.
Alessandro Fortunati Stephen Wiggins 《Celestial Mechanics and Dynamical Astronomy》2016,125(2):247-262
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous integrable part, the system can be cast in an exact normal form, regardless of the properties of the frequency vector. The general case is treated by a suitable adaptation of the finite order normalization techniques usually used for Nekhoroshev arguments. The key point is that the so called “geometric part” is not necessary in this case. As a consequence, no hypotheses on the integrable part are required, apart from analyticity. The work, based on two different perturbative approaches developed by Giorgilli et al., is a generalisation of the techniques used by the same authors to treat more specific aperiodically time-dependent problems. 相似文献
9.
Kenneth R. Meyer 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):159-165
We consider the evolution of the stable and unstable manifolds of an equilibrium point of a Hamiltonian system of two degrees of freedom which depends on a parameter,ν. The eigenvalues of the linearized system are complex for ν < 0 and purely imaginary for ν > 0. Thus for ν < 0 the equilibrium has a two‐dimensional stable manifold and a two‐dimensional unstable manifold, but for ν > 0 these stable and unstable manifolds are gone. We study the system defined by the truncated generic normal form in this situation. One of two things happens depending on the sign of a certain quantity in the normal form expansion. In one case the two families detach as a single invariant manifold and recedes from the equilibrium as ν tends away from 0 through positive values. In the other case the stable and unstable manifold are globally connected for ν < 0 and the whole structure of these manifolds shrinks to the equilibrium as ν → 0 and disappears. These considerations have interesting implications about Strömgren's conjecture in celestial mechanics and the blue sky catastrophe of Devaney. 相似文献
10.
Abstract— Thermodynamic calculations of metastable equilibria were used to evaluate the potential for abiotic synthesis of aliphatic and polycyclic aromatic hydrocarbons (PAHs) in the martian meteorite Allan Hills (ALH) 84001. The calculations show that PAHs and normal alkanes could form metastably from CO, CO2, and H2 below approximately 250–300°C during rapid cooling of trapped magmatic or impact‐generated gases. Depending on temperature, bulk composition, and oxidation‐reduction conditions, PAHs and normal alkanes can form simultaneously or separately. Moreover, PAHs can form at lower H/C ratios, higher CO/CO2 ratios, and higher temperatures than normal alkanes. Dry conditions with H/C ratios less than approximately 0.01–0.001 together with high CO/CO2 ratios also favor the formation of unalkylated PAHs. The observed abundance of PAHs, their low alkylation, and a variable but high aromatic to aliphatic ratio in ALH 84001 all correspond to low H/C and high CO/CO2 ratios in magmatic and impact gases and can be used to deduce spatial variations of these ratios. Some hydrocarbons could have been formed from trapped magmatic gases, especially if the cooling was fast enough to prevent reequilibration. We propose that subsequent impact heating(s) in ALH 84001 could have led to dissociation of ferrous carbonates to yield fine‐grain magnetite, formation of a CO‐rich local gas phase, reduction of water vapor to H2, reequilibration of the trapped magmatic gases, aromatization of hydrocarbons formed previously, and overprinting of the synthesis from magmatic gases, if any. Rapid cooling and high‐temperature quenching of CO‐, H2‐rich impact gases could have led to magnetite‐catalyzed hydrocarbon synthesis 相似文献
11.
12.
The propagation and dissipation of acoustic waves in the lower solar atmosphere is studied. The level of shock formation is computed for various initial conditions. It is shown that shocks form rather low in the atmosphere and that this result does not depend critically on the assumed initial conditions. 相似文献
13.
With the aid of a normal form of a family of measure-preserving mappings in dimension 3, which is deduced in this paper, we prove that there are periodically invariant curves which survive the nonlinear perturbations in the generic case. 相似文献
14.
S. J. Aarseth J. P. Anosova V. V. Orlov V. G. Szebehely 《Celestial Mechanics and Dynamical Astronomy》1994,58(1):1-16
The effects of small changes in the initial conditions of the Pythagorean three-body problem are investigated by computer simulations. This problem consists of three interacting bodies with masses 3, 4 and 5 placed with zero velocities at the apices of a triangle with sides 3, 4 and 5. The final outcome of this motion is that two bodies form a binary and the third body escapes. We attempt to establish regions of the initial positions which give regular and chaotic motions. The vicinity of a small neighbourhood around the standard initial position of each body defines a regular region. Other regular regions also exist. Inside these regions the parameters of the triple systems describing the final outcome change continuously with the initial positions. Outside the regular regions the variations of the parameters are abrupt when the initial conditions change smoothly. Escape takes place after a close triple approach which is very sensitive to the initial conditions. Time-reversed solutions are employed to ensure reliable numerical results and distinguish between predictable and non-predictable motions. Close triple approaches often result in non-predictability, even when using regularization; this introduces fundamental difficulties in establishing chaotic regions. 相似文献
15.
Radial,transverse and normal satellite position perturbations due to the geopotential 总被引：1，自引：0，他引：1
Perturbations in the position of a satellite due to the Earth's gravitational effects are presented. The perturbations are given in the radial, transverse (or alongtrack) and normal (or cross-track) components. The solution is obtained by projecting the Kepler element perturbations obtained by Kaula [Kaula, 1966] into each of the three components. The resulting perturbations are presented in a form analogous to the form of Kaula's solution which facilitates implementation and interpretation. 相似文献
16.
Giuseppe Pucacco 《New Astronomy》2012,17(5):475-482
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward. 相似文献
17.
M. Alvarez-Ramírez J. K. Formiga R. V. de Moraes J. E. F. Skea T. J. Stuchi 《Astrophysics and Space Science》2014,351(1):101-112
We study the fourth-order stability of the triangular libration points in the absence of resonance for the three-body problem when the infinitesimal mass is affected not only by gravitation but also by light pressure from both primaries. A comprehensive summary of previous results is given, with some inaccuracies being corrected. The Lie triangle method is used to obtain the fourth-order Birkhoff normal form of the Hamiltonian, and the corresponding complex transformation to pre-normal form is given explicitly. We obtain an explicit expression for the determinant required by the Arnold-Moser theorem, and show that it is a rational function of the parameters, whose numerator is a fifth-order polynomial in the mass parameter. Particular cases where this polynomial reduces to a quartic are described. Our results reduce correctly to the purely gravitational case in the appropriate limits, and extend numerical work by previous authors. 相似文献
18.
Kenneth H. Schatten 《Solar physics》2009,255(1):3-38
Photospheric ephemeral regions (EPRs) cover the Sun like a magnetic carpet. From this, we update the Babcock – Leighton solar
dynamo. Rather than sunspot fields appearing in the photosphere de novo from eruptions originating in the deep interior, we consider that sunspots form directly in the photosphere by a rapid accumulation
of like-sign field from EPRs. This would only occur during special circumstances: locations and times when the temperature
structure is highly superadiabatic and contains a large subsurface horizontal magnetic field (only present in the Sun’s lower
latitudes). When these conditions are met, superadiabatic percolation occurs, wherein an inflow and downflow of gas scours
the surface of EPRs to form active regions. When these conditions are not met, magnetic elements undergo normal percolation,
wherein magnetic elements move about the photosphere in Brownian-type motions. Cellular automata (CA) models are developed
that allow these processes to be calculated and thereby both small-scale and large-scale models of magnetic motions can be
obtained. The small-scale model is compared with active region development and Hinode observations. The large-scale CA model offers a solar dynamo, which suggests that fields from decaying bipolar magnetic regions
(BMRs) drift on the photosphere driven by subsurface magnetic forces. These models are related to observations and are shown
to support Waldmeier’s findings of an inverse relationship between solar cycle length and cycle size. Evidence for significant
amounts of deep magnetic activity could disprove the model presented here, but recent helioseismic observations of “butterfly
patterns” at depth are likely just a reflection of surface activity. Their existence seems to support the contention made
here that the field and flow separate, allowing cool, relatively field-free downdrafts to descend with little field into the
nether worlds of the solar interior. There they heat by compression to form a hot solar-type Santa Ana wind deep below active
regions. 相似文献
19.
Simon P. Goodwin 《Monthly notices of the Royal Astronomical Society》1998,294(1):47-60
N -body simulations are made with a variety of initial conditions, in particular clumpy and flattened distributions, to attempt to constrain the possible initial conditions of globular clusters, using the observations that young LMC globular clusters appear relaxed after only 20 to 40 Myr. It is found that violent relaxation is able to erase most of the initial substructure in only ≈ 6 crossing times. However, initially very clumpy distributions (≲ 100 clumps) form clusters that are too concentrated to resemble real globular clusters. Such clusters also often have large clumps in long-lasting (≳ 30 crossing times) orbits which do not appear in observed cluster profiles. It is also found that even modest amounts of initial flattening produce clusters that are too elliptical to resemble real globular clusters. In such a scenario, cloud–cloud collisions and similar energetic processes would be unlikely to produce sufficiently spherical globular clusters. It is suggested that globular clusters form from roughly spherical initial conditions with star formation occurring either smoothly or in many small clumps. 相似文献
20.
This paper describes an algorithm which brings a regularizable polynomial perturbation of a three degree of freedom Kepler problem into a normal form which Poisson commutes with the Kepler Hamiltonian. We illustrate the alogrithm with an example: the quadratic Zeeman effect. For other applications of this algorithm see [1],[4], and [5]. The authors have written a program in MAPLE which implements the constrained normal form. 相似文献